Beginnings

Abstract

In the ranks of the outstanding mathematicians of the nineteenth century the name of Bernhard Riemann occupies an illustrious place. Although his career lasted only fifteen years, he made an enormous contribution to almost all areas of mathematics. He worked on the theory of the integral, the theory of functions of a complex variable, geometry, calculus of variations, the theory of electricity, and other subjects. While this short list attests to his multifaceted talents, itdoes not begin to suggest the power of his mind and his striking originality. Practically all of Riemann’s articles contain completely new ideas, such as the introduction of the concept of Riemann surfaces, which provided the foundation for contemporary complex analysis and topology. The value of Riemann’s work is significantly greater than the numerous concrete results he achieved; his exceptionally fruitful ideas stimulated further developments not only in mathematics but also in mechanics, physics, and the philosophy of the natural sciences as a whole.